it is known that the solution of a single soliton from the KdV equation is also a solution of the simpler travelling wave equation: \(u_t = -c u_x\) , see [1]} and figure REF . So trying to discover the underlying equation from an analytical of KdV with a single soliton like,
\(u(x,t) = \frac{c}{2\cosh (\sqrt{c}\frac{x-ct}{2})}\) 
